It was Carlyn's point, but I agree with her. I think you conflate, pursuit with control. Using your own words, "We choose, we pursue, right?"

More men chase women than women chase men. Catlyn's point was, "women control sexual selection" because they choose whom to sleep with way more often than men do.

If men were more discriminating (your further point) then the control would be equal. But that is not the situation right now. Right now women control sexual selection.